Problem: Complete the equation of the line through $(3,-8)$ and $(6,-4)$. Use exact numbers. $y=$
Solution: Let's find the slope: $\begin{aligned} \text{Slope}&=\dfrac{-4-(-8)}{6-3} \\\\ &=\dfrac{4}{3} \end{aligned}$ The equation is $y=\dfrac{4}{3}x+b$ for some $b$. Let's plug the point $({6},{-4})$ to find $b$ : $\begin{aligned} y&=\dfrac{4}{3} x+b \\\\ {-4}&=\dfrac{4}{3}({6})+b \\\\ -4&=8+b \\\\ -12&=b \end{aligned}$ The equation is $y=\dfrac{4}{3}x -12$.